When connecting a PS3 to an HD TV, is there a major advantage to using HDMI instead of component video cables?

It generally depends on the display and player, but the differences shouldn't be too noticeable.

Of course, HDMI can simplify the cable situation. If you don't have a receiver, just the one HDMI cable will carry audio and video to the TV. Even with a receiver, if it can process audio (not all HDMI receivers can), you can just run one cable to the receiver and another to the display.

HDMI is also required for upscaling of protected DVDs (most commercial discs), but the PS3 can't do that yet.

BTW, could you delete your other thread?

AV MULTI OUT is analog, HDMI OUT is digital. I noticed that the colors are more correct using HDMI OUT. (And yes, both are labeled with capital letters)

Were either of these outputs calibrated when you eyeballed the color difference?

Yes.

I noticed the above as well. There was also less color bleed and whites were whiter and blacks blacker.

Is it also true that you cannot watch Blu-Ray discs in 1080p without HDMI? 1080i is the highest you can get with component. Am I wrong about that?

that is correct, I believe.

Depends on the player. So far, I think that is true for all of them. But it is possible someone could make one with 1080p-component capability. (ICT could also be an issue if encoded on the discs, so far not)

Of course, if your TV is 1080p it may already be deinterlacing that 1080i signal.